Tail asymptotics for the total progeny of the critical killed branching random walk

Abstract

We consider a branching random walk on $\mathbb{R}$ with a killing barrier at zero. At criticality, the process becomes eventually extinct, and the total progeny $Z$ is therefore finite. We show that the tail distribution of $Z$ displays a typical behaviour in $(n{\ln }^2(n){)}^{-1}$, which confirms the prediction of Addario-Berry and Broutin.

references added

References in corpus (3)

• The genealogy of branching Brownian motion with absorption
• The number of absorbed individuals in branching Brownian motion with a barrier
• Total progeny in killed branching random walk